Annexe A : Formulaire
295
⎧
⎪ ⎪ ⎨
⎪ ⎪ ⎩
−∇p + ρ g −
μ
K
V = 0
(ρ c p ) f
∂ T
∂t
+ (ρ c p )
∗ V · ∇T = ∇ · (λ ∇T ) + q
• Couche limite, d´ efinitions
ep. de deplacement δ ∗ =
� δ
0
�
1 −
ρ u
ρ e u e
�
dz
ep. de qte de mouvemment θ =
� δ
0
ρu
ρ e u e
�
1 −
u
u e
�
dz
• Equations de la couche limite
∂ u
∂ x
+
∂ w
∂ z
= 0
u
∂ u
∂ x
+ w
∂ u
∂ z
= −
1
ρ
∂ p
∂ x
+ ν
∂ 2 u
∂ z 2
u
∂ T
∂ x
+ w
∂ T
∂ z
=
λ
ρ c p
∂ 2 T
∂ z 2
∂ p
∂ z
= 0
p +
1
2
ρu
2
e = Cte a l
� exterieur
• Equation de Blasius
2 f
���
+ f f
��
= 0
f
�
(0) = 0, f (0) = 0, f
�
(∞) = 1
• Turbulence : hypoth` ese de Boussinesq
k = 0.5u
�
i u
�
i , ε = ν
∂ u �
i
∂ x j
∂ u �
i
∂ x j
−ρ
�
v
� ⊗ v
� −
2
3
k I
�
= μ t
�
∇V + ∇
t
V −
2
3
∇ · V I
�
• Mod` ele (k − ε)
∂ k
∂t
+ V · ∇k = ∇ ·
��
ν +
ν t
σ k
�
∇k
�
+ ν t ∇V :
�
∇V + ∇
t
V
�
− ε
∂ ε
∂t
+ V · ∇ε = ∇ ·
��
ν +
ν t
σ ε
�
∇ε
�
+C 1
ε
k
ν t ∇V :
� ∇V + ∇
t
V
�
−C 2
ε 2
k
ν t =
μ t
ρ
= C μ
k 2
ε